通过深度展开学习替换分裂吉布斯扩散后验采样中的MCMC
Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding
- Weizmann Institute of Science（魏茨曼科学研究所）
- Northeastern University（东北大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出用深度展开网络替换分裂吉布斯采样中的MCMC步骤，通过ODE扩散实现高斯去噪更新，在非线性相位恢复中实现更低成本的扩散后验采样。
AI中文摘要：
分裂吉布斯采样通过解耦先验和似然计算，实现了对一般非线性逆问题的扩散后验推断，允许预训练的扩散先验在不同测量模型间复用。然而，其似然更新通常依赖迭代MCMC，这可能会阻碍并行化、需要针对特定算法的调参，并产生大量计算成本。在本工作中，我们提出一种基于学习的框架来替换这一MCMC步骤，方法是将两个吉布斯更新重新表述为高斯去噪问题，并通过ODE扩散实现。先验步骤复用预训练的去噪器，而似然去噪器则通过轻量级深度展开网络利用已知的似然结构。在非线性相位恢复上的实验表明，所提方法作为基于MCMC的分裂吉布斯在较低似然更新成本下的替代方案是有效的。
英文摘要：
Split Gibbs sampling enables diffusion posterior inference for general nonlinear inverse problems by decoupling prior and likelihood computations, allowing a pretrained diffusion prior to be reused across measurement models. However, its likelihood update often relies on iterative MCMC, which can hinder parallelization, require algorithm-specific tuning, and incur substantial computational cost. In this work, we propose a learning-based framework to replace this MCMC step by reformulating both Gibbs updates as Gaussian denoising problems and implementing them through ODE diffusion. The prior step reuses a pretrained denoiser, while the likelihood denoiser exploits known likelihood structure through a lightweight deep-unfolded network. Experiments on nonlinear phase retrieval demonstrate the effectiveness of the proposed method as an alternative to MCMC-based split Gibbs at lower likelihood-update cost.
